Department of Mathematics
For j ≤ k, the L(j, k)-labeling arose from code assignment problem. That is, let j, k and m be positive numbers, an m-L(j, k)-labeling of a graph G is a mapping f : V(G) → [0, m] such that | f (u)− f (v)| ≥ j if d(u, v) = 1, and | f (u)− f (v)| ≥ k if d(u, v) = 2. The span of f is the difference between the maximum and the minimum numbers assigned by f . The L(j, k)-labeling number of G, denoted by λ j,k (G), is the minimum span over all L(j, k)-labelings of G. The kth power G k of an undirected graph G is the graph with the vertex set of G in which two vertices are adjacent when their distance in G is at most k. In this paper, the L(j, k)-labeling numbers of P 2 n are determined for j ≤ k.
L(j, k)-labeling, Path, Square of path, Code assignment
Source Publication Title
AKCE International Journal of Graphs and Combinatorics
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Open Access funded by Kalasalingam University
Link to Publisher's Edition
Wu, Qiong, and Wai Chee Shiu. "L(j, k)-labeling numbers of square of paths." AKCE International Journal of Graphs and Combinatorics 14.3 (2017): 307-316.